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Analysis of gas turbine integrated cogeneration plant: Process integration approach
Applied Thermal Engineering 78 (2015) 118e128
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Analysis of gas turbine integrated cogeneration plant: Process integration approach Mukund H. Bade*, Santanu Bandyopadhyay Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, Maharashtra, India
h i g h l i g h t s Methodology for direct integration of gas turbine, regenerator, and process plant. Integrated system analysis plotted on turbine pressure ratio vs. power to heat ratio. Regions of integration are identified on this new diagram. Variations of energy utilization factor and fuel energy saving ratio are indicated. Optimal sizing of integrated gas turbine for retrofitting and grassroots design.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 September 2014 Accepted 12 December 2014 Available online 23 December 2014
Cogeneration is defined as generation of two forms of energy viz. heat and work using single primary fuel. Cogeneration or combined heat and power (CHP) is important in improving energy efficiency of the overall plant and in reducing environmental pollution. A methodology, based on pinch analysis, is proposed in this paper to integrate gas turbine and regenerator with a process plant to minimize fuel consumption. Thermodynamic analysis of gas turbine integrated CHP plant is presented on gas turbine pressure ratio versus power to heat ratio diagram. On this novel diagram, limits of integration are identified and various regions of integration are represented. Additionally, contour plots of energy utilization factors and fuel energy saving ratios are represented on this diagram for optimal integration of gas turbine with a process plant. It is interesting to note that though the contour plots of energy utilization factors and fuel energy saving ratios differ significantly, loci of the maximal energy utilization factor and the maximal fuel energy saving ratio are identical. Optimum sizing of gas turbine integrated cogeneration plant for grassroots design and retrofitting are performed based on these diagrams. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Gas turbine integration Cogeneration Pinch analysis Thermodynamic analysis Process integration
1. Introduction To deal with the challenges such as depleting fossil fuel reserves, increasing pollution due to greenhouse gases, adverse effects of climatic changes, need for sustainable development, etc., researchers and engineers are striving hard to develop new tools and techniques for energy saving by improving energy efficiency and reducing energy losses. Cogeneration is one such option to improve energy efficiency by reducing exhaust energy loss. Cogeneration or combined heat and power (CHP) system is defined as generation of process heat and shaft work from a single fuel source to improve
* Corresponding author. Department of Mechanical Engineering, SV National Institute of Technology, Surat 395 007, Gujarat, India. Tel.: þ91 261 2201852; fax: þ91 261 2228394. E-mail address: [email protected] (M.H. Bade). http://dx.doi.org/10.1016/j.applthermaleng.2014.12.024 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
energy utilization in a process industry. Gas turbine based cogeneration plant (GTCP) is one of the important cogeneration plants with less pollution [1]. Thermal energy of the exhaust flue gas from gas turbine may be used for process heating. Low capacity gas turbines (typically, less than 50 MW) are suitable for cogeneration due to low capital cost and less mechanical complexity [2,3]. Various configurations of cogeneration plants have been analyzed through different techniques such as exergy analysis, thermoeconomics, physical insight based pinch analysis, R-curve analysis and mathematical optimization (mixed integer linear programming and non linear programming). Renirie [4] analyzed GTCP with various configurations of heat recovery steam generators (HRSGs) along with back pressure and condensing steam turbines. Kenney [5] introduced the concept of R-curve for optimal design of various cogeneration plants. R-curve is a plot of energy utilization factor (EUF) versus net power to heat ratio (R). Horlock [6] investigated
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thermo-economics of various cogeneration systems including gas turbine without regeneration. Hashem [7] presented thermoeconomic analysis of the GTCP used for refinery. Axelsson et al. [8] proposed graphical methodology for emission reduction and analytical approach for minimum cost of GTCP. Manninen and Zhu [9] presented mixed integer linear programming (MILP) formulation for optimal integration of gas turbine with existing site. Najjar [1] reviewed advanced thermodynamic cycles for GTCP. Lucas [10] developed a methodology to study dependence of the primary energy savings on different technical criteria for cogeneration plant. Bruno et al. [11] reported analysis based on experimental results of micro-GTCP. Ernst and Balestieri [12] proposed methodology to incorporate fluctuating power and heat demands for optimal design of cogeneration plants. Kamate and Gangavati [13] discussed various cogeneration plants generally used in sugar industry. Aguilar et al. [14] determined performance parameters such as energy savings, reduction of pollution, and increasing profitability of GTCP with HRSG based on experimental data. Pinch analysis was proposed as a thermodynamic tool to analyze energy systems. Technique of pinch analysis have been successfully utilized to address cogeneration plants [15e18]. Townsend and Linnhoff [15,16] developed a methodology to size GTCP by matching grand composite curve (GCC) of the process with flue gas profile. Sarabchi and Polley [17], based on pinch analysis, suggested that regeneration should be employed only when heat is excess in flue gas exhaust from gas turbine. However, no methodology was suggested to compute regeneration potential. Bandyopadhyay et al. [18] proposed a pinch based approach to determine cogeneration potential for steam turbine cogeneration plant (STCP). Recently, techniques of pinch analysis are combined with the Rcurve representation [19e23], originally proposed by Kenny [5]. Kimura and Zhu [19] extended the R-curve concept to analyze cogeneration plants for retrofitting and grassroots cases. Varbanov et al. [20] proposed R-curve analysis for STCP, and suggested most appropriate utility system based on energy utilization factor (EUF). Ghannadzadeh et al. [21] proposed cogeneration targeting for site utility system using iterative method. Karimkashi and Amidpour [22] proposed plots of R-curve, R versus total cost, and R versus emission factor for design of cogeneration plants. For STCP, R-curve concept based on exergo-economic and exergo-environmental parameters are proposed by Navid et al. [23]. It may be noted that most of these works are directed towards analyzing STCP on Rcurve. Growing importance of GTCP necessitates appropriate thermodynamic optimization of such systems. It is important to develop an appropriate methodology to integrate gas turbine system with process plant. Primary objective of this paper is to propose such a methodology for appropriate integration of gas turbine, regenerator, and process streams and thereby reduce the overall fuel consumption. It may also be noted that due to significant difference in qualities of thermal energy and shaft work, a single metric is not always sufficient to analyze a CHP system. In this paper, a methodology based on pinch analysis is proposed to integrate gas turbine and regenerator with a process plant to minimize fuel consumption. Thermodynamic analysis of gas turbine integrated CHP plant is presented on novel diagram of gas turbine pressure ratio versus power to heat ratio diagram. Additionally, contour plots of energy utilization factors and fuel energy saving ratios are represented on this diagram for optimal
FESR ¼ 1
119
integration of gas turbine with a process plant. Optimum sizing of gas turbine integrated cogeneration plant for grassroots design and retrofitting are performed based on these diagrams. 2. Gas turbine based cogeneration plant (GTCP) Fig. 1 presents the schematic of GTCP with various components. Inlet air of mass flow rate ma (at ambient temperature, Ta and pressure, Pa) is compressed until pressure Paco (with a corresponding temperature of Taco) is reached. Then, air is heated in regenerator up to temperature Tareo using flue gas. Subsequently, preheated compressed air (Tareo) is used to burn fuel of mass flow rate mf in combustion chamber. The product of combustion termed as flue gas (mass flow rate mg) at a specified maximum temperature (Tgtm) is expanded in gas turbine to generate net work of WCG. The flue gas at gas turbine exit temperature (Tgto) supplies heat to the process streams and the regenerator. Thermal energy available in flue gas at gas turbine exhaust is always greater than or equal to required process heat duty (QP). This is achieved by maintaining mass flow rate of flue gas greater than or equal to the minimum mass flow rate required to satisfy process heat duty. The surplus energy available in flue gas at gas turbine exhaust is recirculated back into combustion chamber through regenerator (Qreg) as shown in Fig. 1. 2.1. Thermodynamic performance parameters As cogeneration involves two different forms of useful energies (viz. heat and power), it is difficult to define a single metric, as the qualities (according to the second law of thermodynamics) of these useful energies are different. To analyze the performance of cogeneration plants, following thermodynamic metrics are used: power to heat ratio (R), energy utilization factor (EUF), and fuel energy saving ratio (FESR) [6]. It may be noted that various other metrics are also proposed in literature. However, EUF and FESR are the two most important and widely used metrics. Power to heat ratio (R) is the ratio of net mechanical power output to the rate of process heat requirement.
R¼
net mechanical power output rate of process heat requirement
(1)
Energy utilization factor (EUF) [6] is the ratio of total useful energy (addition of the net mechanical power output and supplied process heat) to the total fuel energy supplied. Though, EUF recognizes importance of heat (thermal energy), it gives equal importance to heat and mechanical power, and not differentiate based on the second law of thermodynamics. It is used to plot Rcurves, initially proposed by Kenney [5], for thermodynamic analysis of various cogeneration plants.
EUF ¼
net mechanical power output þ process heat total fuel energy supplied
(2)
Fuel energy saving ratio (FESR) [6] is ratio of savings in fuel energy required to meet given mechanical power and heat by a CHP compared to conventional power plant and boiler separately supplying same amount of mechanical power and heat, to fuel energy required by conventional power plant and boiler for same output as that of CHP.
fuel energy required for cogeneration plant to generate power Wnet and heat QP fuel energy required for conventional plants to generate same power Wnet and heat QP
(3)
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Fig. 1. Schematic of gas turbine integrated cogeneration system.
Nesheim and Ertesva [24] called it relative primary energy savings. According to this criterion, two different cogeneration plants in terms of fuel energy savings can be compared. It also indicates societal benefits. 3. Problem definition The streams data of a process plant such as inlet, outlet temperatures, and heat capacity rates are given. The design data of gas turbine such as ambient temperature, maximum gas turbine temperature, specific heats and specific heat ratio of air and flue gas respectively, and lower calorific value of fuel are also known. GTCP generates work and supplies heat available in flue gas at the gas turbine exhaust to satisfy the complete hot utility requirement of the process plant. It is assumed that the heat available in the exhaust flue gas is always greater than or equal to the process heat requirement. This is accomplished by maintaining flue gas flow equals to or higher than the minimum required to satisfy the process heat. Regenerator is provided to improve the overall efficiency of the cogeneration system by preheating compressed air with the exhaust flue gas. The thermodynamic properties of air and flue gas such as specific heat capacities and ratios of specific heat capacities are determined at average temperature and are assumed constant. The objective is to develop a methodology to integrate the gas turbine, regenerator, and the process plant to minimize the overall fuel consumption. 4. Targeting of GTCP for minimum fuel consumption
ratio (Rmin). This minimal integration is analyzed in this subsection. For a fixed pressure ratio of gas turbine, flue gas temperatures at exit of compressor and turbine are determined using ideal gas law for known respective inlet temperatures and efficiencies. The process plant GCC is established using classical problem table algorithm (PTA) [26] or using modified problem table algorithm (MPTA) [27] at given minimum approach temperature and process streams data. The minimum flue gas flow rate can be targeted graphically by matching flue gas line drawn from flue gas temperature at gas turbine exit with process GCC [25,28], as shown in Fig. 2. The minimum mass flow rate of flue gas (mgmin) is given by following equation:
mgmin ¼
Q Qk p Cpg Tgto Tk DT 2
where, Qk and Tk are coordinates of one of the vertexes from process plant GCC and Cpg is specific heat capacity at constant pressure of flue gas. The point at which flue gas line touches process GCC is known as utility pinch (point 3 in Fig. 2) and temperature at that point termed as utility pinch temperature (Tp). However, the utility pinch point is not known a priori. Since utility pinch point is going to form at one of the vertexes of process plant GCC, flue gas (mgmin) can be calculated following Equation (4), for each vertex (k ¼ 1, …,l). The maximum of mass flow rate of flue gas calculated for each vertex represents the minimum mass flow rate of flue gas (mgmin). Mass balance of flue gas flow rate can be written as:
ma þ mf ¼ mg
An analytical methodology for energy integration of gas turbine and regenerator into process plant is developed in this section for the minimum fuel consumption. Methodology proposed by Varghese and Bandyopadhyay [25] for energy integration of fired heater with overall process is appropriately modified to apply for integration of gas turbine and regenerator into process plant. 4.1. Targeting GTCP at minimum power to heat ratio (Rmin) The heat available in flue gas at the outlet of gas turbine is transferred directly to cold streams of the process plant in process exchangers and to the compressed air in regenerator. If the heat availability from the flue gas at the exit of gas turbine is not sufficient to satisfy total process heat requirement then integration is termed as insufficient integration. The additional heat, in case of insufficient integration, can be provided either through auxiliary heating or by increasing flue gas flow rate. In this paper, insufficient integration is not considered. The minimum flow rate of flue gas, at which process heat is satisfied completely, is considered as the minimal integration and is represented by minimum power to heat
(4)
Fig. 2. Targeting of flue gas flow rate by matching with process plant GCC.
(5)
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The regenerated compressed air (at temperature, Tareo and mass flow rate, ma) is used for burning fuel in the combustion chamber. The flue gas temperature at exit of combustion chamber is Tgtm. The energy balance for combustion chamber [29] is given as:
ðTareo Ta Þma Cpa þ CV*hcc mf ¼
Tgtm Ta mg Cpg
(6)
where, CV is net calorific value of fuel, Cpa is specific heat capacity at constant pressure of air, and hcc is combustion efficiency. Ta is ambient temperature and not air temperature. Pinch analysis may be applied to determine compressed air temperature at regenerator outlet (Tareo), using the concept of the utility GCC [28]. Utility GCC is formed using utility streams such as flue gas and compressed air of integrated gas turbine. Fig. 3 illustrates the hot utility (temperature of flue gas from gas turbine exit, Tgto to stack, Tls) and cold utility (temperature of compressed air from compressor delivery, Taco to regenerator outlet, Tareo) composite curves. Similar to process plant GCC, the utility GCC is a plot of the enthalpy difference between the utility composites as shown in Fig. 3. It should be noted that the utility GCC is shown as reflected utility GCC (mirror image of utility GCC about vertical axis, see Fig. 3). This helps in matching it with process GCC to balance utility requirement as shown in Fig. 4. The matched process plant GCC and reflected utility GCC with other details such as hot and cold utility requirement, utility pinch points, and stack loss are shown in Fig. 4. All GCCs are plotted on shifted temperature scale with minimum approach temperature, DT. Air is heated from compressor delivery temperature (Taco) to regenerator temperature (Tareo) by flue gas. From energy balance at utility pinch point, regenerator outlet temperature, Tareo is determined as:
mg Cpg Tareo ¼
Tgto Ti DT 2 ma Cpa
Q P Qi
þ Tia
DT 2
(7)
where, Tia is compressed air temperature. If Ti < (Taco þ DT/2), then Tia ¼ (Taco þ DT/2), else Tia ¼ Ti. In general, Tia ¼ Maximum [(Taco þ DT/2), Ti]. The regenerator outlet temperature of air (Tareo) can be increased utmost up to flue gas temperature at gas turbine exit with approach temperature (Tgto DT). If compressor delivery temperature is higher than flue gas temperature at gas turbine exit, there is no regeneration and the regenerator outlet temperature of air (Tareo) is equal to compressor delivery temperature and is not determined by Equation (7). Once Tareo is determined, fuel consumption (mf) can be calculated using mass and energy balance of combustion chamber (Equation (6)). The mass flow rate of fuel consumption is determined at the minimum flue gas flow rate is represented as mfmin. Substituting Equations (4), (5) and (7) into Equation (6) and simplifying, mass flow rate of fuel consumption is given as:
QP
mfmin ¼
Qk Q P Tgto eTk
DT 2
Tgtm Tgto Ta þ Ti þ DT 2 CVhcc Cpa Tia
Cpa Cpg
DT 2
Fig. 3. Generation of utility GCC from utilities composite curves.
Fig. 4. Targeting of fuel consumption by matching of utility GCC with process plant GCC.
GCC. However, the utility pinch point is not known a priori. Since pinch is going to form at one of the vertexes of process plant GCC, fuel consumption (mfmin) can be calculated following Equation (8), for each vertex (i ¼ 1, …, l). The maximum of mass flow rate of fuel calculated for each vertex represents the minimum mass flow rate of fuel consumption (mfmin) for optimal integration of GTCP. The utility GCC touched at any of the vertex without intersection with process plant GCC forms optimal integration of gas turbine, regenerator, and process plant. This condition is satisfied for one of
Tia Ta
DT 2
þ Q p Qi (8)
Ta
where, Qi and Ti are the coordinates of one of the vertexes of process GCC and Tia is temperature of compressed air. QP is total process heat required and equals to the total hot utility of process plant
the vertexes, at which mass flow rate of fuel is the maximum, represents utility pinch. The other parameters R, EUF, and FESR are determined as follow:
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R¼
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mg Cpg Tgtm Tgto ma Cpa ðTaco Ta Þ Qp
EUF ¼
mg Cpg Tgtm Tgto ma Cpa ðTaco Ta Þ þ Qp mf CV
(9)
by modifying equations provided in Section 4.1. At Rc, the compressed air temperature at regenerator outlet is equal to (Tgto DT), is substituted in Equation (7), and mass flow rate of air is determined by energy balance as:
(10) mg Cpg ma ¼
FESR ¼ 1
mf CV mg Cpg ðTgtm Tgto Þ ma Cpa ðTaco Ta Þ hPP
Q
(11)
þ hp B
Tgto Ti DT Q Q P i 2 Cpa Tgto Tia DT
Substituting Equations (5), (9) and (12) in Equation (6), and Tareo is replaced with (Tgto DT), Rc is calculated to be:
8 9 3 2 > > > > DT > > ð Taco eTa Þ Tgto eTi 2 > > 7 6 > > CV*h > > cc 7 6 > > T e T DT eT T gto a 4 gtm gto DT > Cpa > 5 T T > > gto ia 2 > > > > < = QP Qi þ ðTaco Ta Þ Rc ¼ 3 2 > QP Tgto eTia DT > > > CV*hcc DT > > e Tgto þDT þTa > > Cpa > > 7 6 Tgto eTi 2 > > CV*h > > cc 7 6 > > T e T e þ gtm a > > 5 4 Cpg Tgto e Tia e DT > > 2 > > : ;
For a given pressure ratio, Equation (9) determines R at the minimum flue gas flow rate, denoted as Rmin. Similarly, for all pressure ratios, minimum fuel consumption (mfmin), Rmin, EUF, and FESR are determined. Procedure of integration of GTCP is summarized as follows (flow chart of the same is shown in Fig. 5): Step 1 The process plant data and minimum approach temperature are given. With the help of MPTA [27] determine utilities requirements and plot process plant GCC. Step 2 For a specified pressure ratio of gas turbine, calculate outlet temperatures of compressor and gas turbine for known respective inlet temperatures and efficiencies. Step 3 Determine minimum mass flow rate of flue gas (mgmin) by Equation (4). Step 4 Determine mfmin from Equation (8). Also, compute other parameters such as Rmin, EUF, and FESR from Equations (9)e(11) respectively. Step 5 Similarly, determine mfmin, Rmin, EUF, and FESR for various pressure ratios and analyze thermodynamic performance of GTCP.
4.2. Targeting GTCP at critical regeneration limit (Rc) Heat availability increases with increasing mass flow rate in flue gas at any pressure ratio. This increased heat in flue gas, above the minimum required value, can be utilized through regeneration. By increasing flow rate of flue gas, compressed air can be heated maximum up to flue gas temperature at gas turbine exit with minimum approach temperature i.e. (Tgto DT). Increasing flue gas flow rate beyond a critical limit (mg at Rc) increases the stack losses and thereby, deteriorates overall energy efficiency of the system. The flue gas mass flow rate, at which compressed air is heated in regenerator up to (Tgto DT), is represented as critical flue gas flow rate, and corresponding critical R is denoted by Rc. The regeneration at Rc is termed as critical regeneration, where regeneration temperature is maximum possible with critical flue gas flow rate. It may be noted that the flue gas flow rate may be higher than the critical value if demand of shaft work is higher (i.e., R is higher than Rc). The critical mass flow rate of fuel consumption and Rc are determined
(12)
(13)
where, Qi and Ti are the coordinates of one of the vertexes from process GCC. Tia is same as mentioned in Section 4.1. Similar to Equation (8), utility pinch point is not known a priori, so Rc is determined following similar procedure. The regeneration is possible up to a pressure ratio, at which compressor delivery temperature (Taco) is equal to gas turbine exit temperature (Tgto) with approach temperature. This pressure ratio is referred as regeneration limiting pressure ratio (PRlimr). Beyond regeneration limiting pressure ratio, Rc equals to Rmin. Now, mf is established from Equations (5), (9), (12) and (13). The EUF and FESR are calculated from Equations (10) and (11) respectively.
4.3. Illustrative example 1 Consider GTCP with design data given in Table 1. Note that the net work generated by gas turbine is specified and is varied to illustrate the proposed methodology. The minimum approach temperature for process plant and utility GCC is 50 K. The hot utility requirement is 5000 kW with shifted pinch temperature of 398 K for the minimum approach temperature of 50 K. The problem is a threshold problem with no cold utility requirement. Data provided in Table 1 for gas turbine design is utilized to determine temperatures of air at compressor delivery and of flue gas at gas turbine exit. Theoretically possible minimum and maximum pressure ratios for GTCP are 1 and 105.8, respectively. Theoretical maximum pressure of gas turbine is constrained by the maximum temperature of process heating or compressor delivery temperature. In current problem, the maximum pressure ratio is constrained by the compressor delivery temperature, as above this pressure ratio compressor out let temperature is higher than turbine inlet temperature. The operating pressure of gas turbine plant is well below the theoretical maximum pressure ratio. At Rmin, if temperature of compressed air is less than actual process pinch temperature then compressed air is regenerated maximum up to actual process pinch temperature. At the minimum flue gas flow rate, regeneration is not achievable for pressure ratio higher than 1.95 due to Taco (Ti DT/2). The minimum mass flow rate of flue gas is targeted by using Equation (4). Following flow chart given in Fig. 5 and procedure outlined in Section 4.2, Rmin and Rc are determined appropriately for various pressure ratios.
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Fig. 5. Flow chart for targeting of GTCP at minimum flue gas flow rate.
The plot of pressure ratio (PR) versus R represents curves for Rmin and Rc with various integration regions of GTCP as shown in Fig. 6. As pressure ratio increases, Rmin also increases, and reaches a maximum. It reaches the maximum at a pressure ratio, where net work is highest. Subsequently with increasing pressure ratio further, Rmin decreases continuously still the theoretical maximum pressure ratio (provided theoretical maximum pressure ratio is higher than pressure ratio, at which specific net work is maximum). As pressure ratio increases, Rc also increases, reaches a maximum and then decreases till it coincides with Rmin curve. Rc and Rmin curves coincide with each other when the limiting regeneration pressure ratio is reached. For this example, limiting regeneration pressure ratio (PRlimr) is 15.3. Above limiting regeneration pressure ratio (PRlimr ¼ 15.3), there is no regeneration region. The region towards left of Rmin curve represents insufficient integration where process heat demand is not satisfied. The region outside of Rc
(towards right), due to high flue gas flow rate and constraint of maximum regeneration temperature, represents high stack loss. The intersection region of Rmin and Rc is feasible region for integration of gas turbine, regenerator, and process plant as shown in Fig. 6. 4.4. Thermodynamic analysis of GTCP To analyze thermodynamic performance of GTCP, variations of EUF and FESR with pressure ratios are studied. To determine contours of EUF and FESR at various pressure ratios by changing flue gas flow rate (mg mgmin), equations developed in previous sub-
Table 1 Gas turbine design data. Maximum gas turbine inlet temperature (Tgtm), K Atmospheric air temperature (Ta), K Gas turbine efficiency (hT) Minimum approach temperature for all GCCs (DT), K Specific heat capacity at constant pressure gas (Cpg), kW/kgK Ratio of specific heat capacities gas (gg) Thermal efficiency of standard plant (hPP) Stream generator efficiency (hB)
1373
298 0.9 50
Specific heat capacity at constant pressure air (Cpa), kW/kgK Process heat duty (Qp), kW Compressor efficiency (hc) Ratio of specific heat capacities air (ga)
1.148 Combustion efficiency of GT (hcc) 1.33 0.36 0.9
Stack temperature (Ts), K Lower calorific value of fuel (CV), kJ/kg
1.005
5000 0.85 1.4
0.98
393 41,000 Fig. 6. Various integration regions for GTCP of example 1.
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sections are modified. From Equations (5) and (7), regeneration temperature is determined to be:
! Tareo ¼
mg Cpg
CVhcc CVhcc DT T DT cc Ta þ CVh T T T T Q þ T þ Q gto gtm a a P i i ia Cpa Cpg Cpa 2 2 CVhcc QP Qi mg Cpg Tgto Ti DT 2 Tgtm þ Ta þ Cpg
where, Qi and Ti are the coordinates of one of the vertexes of process GCC. Calculation of Tia is described in sub-Section 4.1. The regenerator outlet temperature of air (Tareo) can be increased utmost up to flue gas temperature at gas turbine exit with approach temperature (Tgto DT). If compressor delivery temperature is higher than flue gas temperature at gas turbine exit, there is no regeneration and the regenerator outlet temperature of air (Tareo) is equal to compressor delivery temperature. In general, Tareo is determined by following condition:
Tareo ¼
8 > < Taco
procedure to determine data for a range of constant EUF at various pressure ratios.
! > ; : MIN Tareo
Tgto
DT 2
If Tgto Taco otherwise
(15)
Mass flow rates of fuel consumption, and compressed air may be calculated using Equations (5), (6) and (15). Subsequently, R, EUF, and FESR can be determined for any given pressure ratio and flue gas flow rate. Flow chart shown in Fig. 7 represents systematic
(14)
4.4.1. Revisiting example 1 Study the behavior of EUF using PR versus R curve. All data of GTCP and process plant are same as given in example 1. Using procedure given in flow chart (Fig. 7), the data for constant EUF is obtained. The contours of EUF are created by plotting data of various constant EUF on PR versus R plot as shown in Fig. 8. The nature of constant EUF curves for higher values is similar to Rmin curve. The flue gas flow rate is less at lower R, and hence stack loss are lower, results in higher EUF (see Fig. 8 for EUF ¼ 0.8). On the other hand, lower values of constant EUF lines show similar nature as that of Rc curve with higher R (see Fig. 8 for constant EUF at 0.6). Lower EUF indicates higher stack loss due to higher flue gas flow rate. In addition to this, maximum regeneration temperature limit is reached at Rc, so for higher R (>Rc), stack loss are further increased. The highest value of EUF is at pressure ratio 1 and R equal to zero, represented by rhombus in Fig. 8. For pressure ratio 1, GTCP works as fired heater. Procedure of data generation for constant FESR curve is also given in flowchart of Fig. 7. In this, mass flow rate is varied until
Fig. 7. Flow chart to generate contours of EUF/FESR on PR versus R plot.
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125
which remains constant with further increasing R. It is interesting to note that though the contour plots of energy utilization factors and fuel energy saving ratios differ significantly, loci of the maximal energy utilization factor and the maximal fuel energy saving ratio are identical as shown in Fig. 10. The EUF and FESR are given in terms of R as follows:
EUF ¼
Q P ð1 þ RÞ mf CV
FESR ¼ 1 QP
(16)
mf CV
R hPP
þ
(17)
1 hB
From Equations (16) and (17), relationship between EUF and FESR is written as: Fig. 8. Contour of EUF for integrated GTCP of example 1.
FESR ¼ 1 EUF
FESR determined by Equation (11) is matched with fixed FESR. For some of the pressure ratios, there are two values of FESR, as FESR increases from minimum value (corresponding to mgmin) to maximum and then decreases with increase in flue gas flow rate, unlike EUF for a given pressure ratio. The searching two values of FESR for typical pressure ratios are important. The contours of FESR are generated by data of various constant FESR on PR versus R plot as shown in Fig. 9. The contours of FESR start from Rmin curve. With increase in R, pressure ratio for constant FESR curve decreases still it intersects Rc at minimal pressure ratio. Further increasing R, pressure ratio increases continuously, however, R reaches maximum and starts decreasing following nature of Rc curve (see FESR ¼ 0.2 and 0.25 in Fig. 9). A constant FESR curve for large values starts from Rc, and also ends at Rc as shown in Fig. 9 for FESR ¼ 0.35. The highest value of FESR is a point (0.353) represented by rhombus as shown in Fig. 9. The maximum EUF and FESR are determined for various pressure ratios considering flue gas flow rate as variable at a given pressure ratio. This curve starts at pressure ratio equals to 1 and R equals to zero. With increasing pressure ratio, R increases, following Rmin curve up to a pressure ratio, at which specific net work is maximum. Then this curve is shifted to Rc curve, as pressure ratio decreases with increasing R. It leaves Rc curve at pressure ratio 4.53,
Fig. 9. Contour of FESR for integrated GTCP of example 1.
1þR
R hPP
þ
(18)
1 hB
Equation (18) shows that for given R, EUF and FESR are proportional to each other assuming standard power plant and boiler plant efficiencies constant. Due to this, in pressure ratio versus R plot, both curves of maximum EUF and FESR are identical as shown in Fig. 10. In retrofitting case, where process heating is to be implemented, pressure ratio of gas turbine plant is known. The horizontal line dropped from a given pressure ratio, intersects maximum EUF and FESR curve at two places with two values of R to design cogeneration system. As shown in Fig. 10, horizontal line dropped from pressure ratio PR1 intersects maximum EUF and FESR curve at R1 and R2, where R1 < R2. At same pressure ratio, specific work is constant, so lower value of R (R1) represents lower flue gas flow rate and hence lesser stack loss. Designing system at R1 gives higher EUF, which indicates lower fuel consumption with lower operating cost. On the other hand, designing system at R2, represents higher FESR as R2 is at critical regeneration limit. This signifies higher work out and higher societal benefits. There is Pareto optimality between higher EUF and higher FESR based on design objective and hence decision maker's role is important.
Fig. 10. Designing of integrated gas turbine, regenerator, and process plant for example 1.
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Table 2 Process plant data (minimum approach temperature ¼ 50 K). Streams
Ts, K
Tt, K
C, kW/K
Heat duty, kW
H1 H2 H3 C1 C2
675 575 575 315 315
375 375 365 675 575
100 82.5 10 60 120
30,000 16,500 2100 21,600 31,200
For a new design, power to heat ratio (R) can be determined easily. For this value of power to heat ratio (R), there is unique value of the maximum EUF and FESR with corresponding pressure ratio for optimal design of GTCP. If vertical line dropped from a given value of R falls on maximum EUF and FESR curve which is part of Rc curve with higher FESR, else R drops on maximum EUF and FESR curve which is part of Rmin curve with higher EUF and lower fuel consumption. For any R, outside the range of critical regeneration limit (Rc) at maximum EUF and FESR curve (see Fig. 10, Rpl), there is very high stack loss. Similarly, for pressure ratio outside the range of maximum EUF and FESR curve (PR > PRl, see Fig. 10), stack loss is higher. For PR > PRlimr (see Fig. 10), there is no regeneration, and hence very high stack losses.
Fig. 12. Contour of FESR for integrated GTCP of example 2.
Table 2 gives process streams data such as inlet-outlet temperatures, heat capacity rate, and heat duty of the process plant. The minimum approach temperature for all integrations is 50 K. Using MPTA [27], hot and cold utilities requirement are determined to be 5000 and 800 kW respectively with shifted pinch temperature 550 K. The total heat demand of process plant 5000 kW is satisfied by flue gas exhaust from gas turbine by direct heat transfer using counter current heat exchanger. Gas turbine design data given in Table 1 is applied to determine temperatures of compressed air at compressor delivery and flue gas at gas turbine outlet. The procedure given in Section 4 is used to determine various parameters and from them various graphs are plotted. The variation of Rmin and Rc on PR versus R plot represents the different regions of integration as shown in Fig. 11. The overall nature of curves is similar to previously shown for example 1. Compared to example 1, in this example, process pinch temperature and process heat requirements are at elevated temperature. Additionally, it is observed that utility pinch point is changed from one vertex to another
vertex for typical values of pressure ratios and power to heat ratio. The change in pinch point from one vertex to another vertex is termed as shift of pinch point or pinch jump. Due to process heat requirement at elevated temperature, the maximum pressure ratio for integration with process plant is limited up to 19.5. In addition to this, for requirement of process heat at higher temperature, flue gas flow rate required is also high, increasing values of R. The first peak in Rc curve is due to shift of utility pinch point at pressure ratio 6.16 and R to be 4.3. Due to shift of utility pinch point, the pinch point temperature increases, increasing flue gas flow rate, R, and pressure ratio. This results in diverging of remaining part of Rmin and Rc curves outwards as shown in Fig. 11 (see points P1 and P2). The contour for EUF can be generated similar to Fig. 8 (for brevity it is not shown). The contour for FESR is shown in Fig. 12. Due to shift of pinch points, the shape of contour plots are changed, however overall nature is remained same. Additionally, it is observed that maximum EUF and FESR curve plotted on pressure ratio versus R, overlap exactly as shown in Fig. 13. It starts from Rmin curve with pressure ratio equals to 1 and R equals to zero. The maximum EUF and FESR curve moves along Rmin curve, and both R and pressure ratio increases. Then it translates to Rc curve, following Rc curve with increasing pressure ratio and R. At the end, it leaves Rc curve at pressure ratio 4.53 with further increase of R, same as observed earlier for example 1. At higher R, (>Rpl),
Fig. 11. Various integration regions for GTCP of example 2.
Fig. 13. Designing of integrated gas turbine, regenerator, and process plant for example 2.
5. Illustrative example 2
M.H. Bade, S. Bandyopadhyay / Applied Thermal Engineering 78 (2015) 118e128
compared to process heat, power generation is very high, reducing Equation (16) of EUF to the equation of power plant efficiency. This represents integrated gas turbine system behaves as gas turbine power plant with regeneration following characteristics of gas turbine power plant. It is important to note that at lower pressure ratio, the efficiency of gas turbine power plant with regeneration is highest (for example 1 and 2, pressure ratio is 4.53 at 1373 K maximum temperature), similar observation is reported by Saravanamuttoo et al. [29]. In general, GTCP should be designed between optimal pressure ratio (PRopt) at which power plant efficiency is maximum and limiting pressure ratio (PRl) at which specific net work is maximum. There may be tradeoff between gas turbine power plant efficiency, and its size and weight. Gas turbine power plant designed at optimal pressure for maximum efficiency requires higher size and capacity due to lower specific net work. On the other hand, system designed at pressure ratio for maximum specific net work, pressure ratio is higher with heavy compressor and lower efficiency. 6. Conclusion A methodology is proposed to integrate gas turbine and regenerator with process plant directly at minimum fuel consumption. In addition to this, thermodynamic analysis of GTCP with regeneration is presented on gas turbine pressure ratio versus power to heat ratio diagram. On this novel diagram, limits of integration are identified and various regions of integration are presented such as infeasible integration, feasible integration, high stack, and no regenerator. Additionally, contour plots of energy utilization factors and fuel energy saving ratios are represented on this diagram for optimal integration of gas turbine with a process plant. It is interesting to note that though the contour plots of energy utilization factors and fuel energy saving ratios differ significantly, loci of the maximal energy utilization factor and the maximal fuel energy saving ratio are identical. It is noted that GTCP with regeneration is thermodynamically efficient at lower pressure ratios. The proposed analysis (maximum EUF and FESR plot on pressure ratio vs. R) can be used for retrofitting and grassroots design to select optimal configuration of GTCP. In grassroots design of GTCP, for a given R, optimal pressure ratio can be selected based on maximum EUF and FESR. The retrofitting case, for known pressure ratio, there are two values of R. Optimal R can be decided based on the objective of designer such as operating cost to be minimum or fuel energy savings (societal benefits) to be maximum. The shift of pinch point influences the sizing of GTCP as shown by example 2. At very high R, GTCP plant behaves similar to gas turbine plant with regeneration. The maximum EUF and FESR are at maximum power plant efficiency with constant optimal pressure ratio for very high values of R (>Rl). The optimal pressure ratio for maximum power plant efficiency is lower than limiting pressure ratio at which specific net work is maximum. There may be tradeoff between gas turbine power plant efficiency, and its size and weight. Gas turbine power plant designed at optimal pressure for maximum power plant efficiency requires higher size and capacity due to lower specific net work. On the other hand, system designed for maximum specific net work requires high pressure ratio with heavy compressor and low power plant efficiency. Nomenclatures Cp CV m q/Q R
specific heat at constant pressure (kJ/kgK) net calorific value (kJ/kg) mass flow rate (kg/s) heat duty (kW) ratio of power to heat rate
T W
127
temperature (K) mechanical power (kW)
Abbreviations CHP combined heat and power EUF energy utilization factor FESR fuel energy saving ratio GCC grand composite curve GT gas turbine GTCP gas turbine cogeneration plant HRSG heat recovery steam generators MILP mix integer linear programming MPTA modified problem table algorithm PR pressure ratio PTA problem table algorithm STCP steam turbine cogeneration plant UGCC Utility grand composite curve Greek letters g specific heat capacity ratio D difference h efficiency Subscripts a air B boiler c critical cc combustion chamber CG cogeneration co compressor f fuel g flue gas gt gas turbine i intermediate state/indices k index l/lim limiting value lp limiting plant m maximum/modified min minimum o outlet p pinch PP power plant reg regenerator s stack References [1] Y.S.H. Najjar, Gas turbine cogeneration systems: a review of some novel cycles, Appl. Therm. Eng. 20 (2) (2000) 179e197. [2] T. Heppenstall, Advanced gas turbine cycles for power generation: a critical review, Appl. Therm. Eng. 18 (9e10) (1998) 837e846. [3] A. Poullikkas, An overview of current and future sustainable gas turbine technologies, Renew. Sustain. Energy Rev. 9 (5) (2005) 409e443. [4] F.J.L. Renirie, Some asfects influencing the design of gas turbine co-generation plants, Resour. Conserv. 7 (1981) 267e286. [5] W.F. Kenney, Energy Conservation in the Process Industries, Academic Press, 1984. [6] J.H. Horlock, Combined Heat and Power (Thermodynamics and Fluid Mechanics Series), Pergamon Press, Oxford, 1987. [7] H.H. Hashem, Thermal-economic analysis of industrial gas turbine cogeneration plant, Energy Convers. Manag. 32 (5) (1991) 419e424. [8] H. Axelsson, A. Asblad, T. Berntsson, A new methodology for greenhouse gas reduction in industry through improved heat exchanging and/or integration of combined heat and power, Appl. Therm. Eng. 19 (7) (1999) 707e731. [9] J. Manninen, X.X. Zhu, Optimal gas turbine integration to the process industries, Ind. Eng. Chem. Res. 38 (11) (1999) 4317e4329. [10] K. Lucas, On the thermodynamics of cogeneration, Int. J. Therm. Sci. 39 (2000) 1039e1046.
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[11] J.C. Bruno, L.I. Massagues, A. Coronas, Stand-alone and grid-connected performance analysis of a regenerative micro gas turbine cogeneration plant, Proc. Inst. Mech. Eng. Part A J. Power Energy 218 (1) (2004) 15e22. [12] B.M.A. Ernst, P.J.A. Balestieri, Influences of thermal and electric load fluctuations in the cogeneration attractiveness, Appl. Therm. Eng. 26 (14e15) (2006) 1500e1505. [13] S.C. Kamate, P.B. Gangavati, Cogeneration and distributed cogeneration in sugar industries: technology options and performance parameters e a review, Cogener. Distrib. Gener. J. 24 (4) (2009) 6e33. [14] F.J.-E. Aguilar, M.T. García, E.C. Trujillo, J.A.B. Villanueva, F.J.F. Ojeda, Prediction of performance, energy savings and increase in profitability of two gas turbine steam generator cogeneration plant, based on experimental data, Energy 36 (2) (2011) 742e754. [15] D.W. Townsend, B. Linnhoff, Heat and power networks in process design. Part II: design procedure for equipment selection and process matching, AIChE J. 29 (5) (1983) 748e771. [16] D.W. Townsend, B. Linnhoff, Heat and power networks in process design. Part I: criteria for placement of heat engines and heat pumps in process networks, AIChE J. 29 (5) (1983) 742e748. [17] K. Sarabchi, G.T. Polley, Gas turbine direct integration in the context of pinch technology, Chem. Eng. Technol. 25 (8) (2002) 829. [18] S. Bandyopadhyay, J. Varghese, V. Bansal, Targeting for cogeneration potential through total site integration, Appl. Therm. Eng. 30 (1) (2010) 6e14.
[19] H. Kimura, F.X.X. Zhu, R-Curve concept and its application for industrial energy management, Ind. Eng. Chem. Res. 39 (7) (2000) 2315e2335. [20] P. Varbanov, S. Perry, Y. Makwana, X.X. Zhu, R. Smith, Top-level analysis of site utility systems, Chem. Eng. Res. Des. 82 (6) (2004) 784e795. [21] A. Ghannadzadeh, S. Perry, R. Smith, Cogeneration targeting for site utility systems, Appl. Therm. Eng. 43 (2012) 60e66. [22] S. Karimkashi, M. Amidpour, Total site energy improvement using R-curve concept, Energy 40 (1) (2012) 329e340. [23] P. Navid, M.H.K. Manesh, A.M.B. Marigorta, Optimal design of cogeneration system based on exergoenvironmental analysis, Clean Technol. Environ. Policy 16 (6) (2013) 1045e1065. [24] S.J. Nesheim, I.S. Ertesvag, Efficiencies and indicators defined to promote combined heat and power, Energy Convers. Manag. 48 (3) (2007) 1004e1015. [25] J. Varghese, S. Bandyopadhyay, Energy integration of fired heaters into overall processes, Int. J. Environ. Sustain. Dev. 8 (1) (2009) 36e59. [26] B. Linnhoff, J.R. Flower, Synthesis of heat exchanger networks: I. Systematic generation of energy optimal networks, AIChE J. 24 (4) (1978) 633e642. [27] S. Bandyopadhyay, G.C. Sahu, Modified problem table algorithm for energy targeting, Ind. Eng. Chem. Res. 49 (22) (2010) 11557e11563. [28] S.G. Hall, B. Linnhoff, Targeting for furnace systems using pinch analysis, Ind. Eng. Chem. Res. 33 (12) (1994) 3187e3195. [29] H. Saravanamuttoo, G. Rogers, H. Cohen, Gas Turbine Theory, Prentice Hall, New York, 2001.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Analysis of gas turbine integrated cogeneration plant: Process integration approach Mukund H. Bade*, Santanu Bandyopadhyay Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, Maharashtra, India
h i g h l i g h t s Methodology for direct integration of gas turbine, regenerator, and process plant. Integrated system analysis plotted on turbine pressure ratio vs. power to heat ratio. Regions of integration are identified on this new diagram. Variations of energy utilization factor and fuel energy saving ratio are indicated. Optimal sizing of integrated gas turbine for retrofitting and grassroots design.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 September 2014 Accepted 12 December 2014 Available online 23 December 2014
Cogeneration is defined as generation of two forms of energy viz. heat and work using single primary fuel. Cogeneration or combined heat and power (CHP) is important in improving energy efficiency of the overall plant and in reducing environmental pollution. A methodology, based on pinch analysis, is proposed in this paper to integrate gas turbine and regenerator with a process plant to minimize fuel consumption. Thermodynamic analysis of gas turbine integrated CHP plant is presented on gas turbine pressure ratio versus power to heat ratio diagram. On this novel diagram, limits of integration are identified and various regions of integration are represented. Additionally, contour plots of energy utilization factors and fuel energy saving ratios are represented on this diagram for optimal integration of gas turbine with a process plant. It is interesting to note that though the contour plots of energy utilization factors and fuel energy saving ratios differ significantly, loci of the maximal energy utilization factor and the maximal fuel energy saving ratio are identical. Optimum sizing of gas turbine integrated cogeneration plant for grassroots design and retrofitting are performed based on these diagrams. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Gas turbine integration Cogeneration Pinch analysis Thermodynamic analysis Process integration
1. Introduction To deal with the challenges such as depleting fossil fuel reserves, increasing pollution due to greenhouse gases, adverse effects of climatic changes, need for sustainable development, etc., researchers and engineers are striving hard to develop new tools and techniques for energy saving by improving energy efficiency and reducing energy losses. Cogeneration is one such option to improve energy efficiency by reducing exhaust energy loss. Cogeneration or combined heat and power (CHP) system is defined as generation of process heat and shaft work from a single fuel source to improve
* Corresponding author. Department of Mechanical Engineering, SV National Institute of Technology, Surat 395 007, Gujarat, India. Tel.: þ91 261 2201852; fax: þ91 261 2228394. E-mail address: [email protected] (M.H. Bade). http://dx.doi.org/10.1016/j.applthermaleng.2014.12.024 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
energy utilization in a process industry. Gas turbine based cogeneration plant (GTCP) is one of the important cogeneration plants with less pollution [1]. Thermal energy of the exhaust flue gas from gas turbine may be used for process heating. Low capacity gas turbines (typically, less than 50 MW) are suitable for cogeneration due to low capital cost and less mechanical complexity [2,3]. Various configurations of cogeneration plants have been analyzed through different techniques such as exergy analysis, thermoeconomics, physical insight based pinch analysis, R-curve analysis and mathematical optimization (mixed integer linear programming and non linear programming). Renirie [4] analyzed GTCP with various configurations of heat recovery steam generators (HRSGs) along with back pressure and condensing steam turbines. Kenney [5] introduced the concept of R-curve for optimal design of various cogeneration plants. R-curve is a plot of energy utilization factor (EUF) versus net power to heat ratio (R). Horlock [6] investigated
M.H. Bade, S. Bandyopadhyay / Applied Thermal Engineering 78 (2015) 118e128
thermo-economics of various cogeneration systems including gas turbine without regeneration. Hashem [7] presented thermoeconomic analysis of the GTCP used for refinery. Axelsson et al. [8] proposed graphical methodology for emission reduction and analytical approach for minimum cost of GTCP. Manninen and Zhu [9] presented mixed integer linear programming (MILP) formulation for optimal integration of gas turbine with existing site. Najjar [1] reviewed advanced thermodynamic cycles for GTCP. Lucas [10] developed a methodology to study dependence of the primary energy savings on different technical criteria for cogeneration plant. Bruno et al. [11] reported analysis based on experimental results of micro-GTCP. Ernst and Balestieri [12] proposed methodology to incorporate fluctuating power and heat demands for optimal design of cogeneration plants. Kamate and Gangavati [13] discussed various cogeneration plants generally used in sugar industry. Aguilar et al. [14] determined performance parameters such as energy savings, reduction of pollution, and increasing profitability of GTCP with HRSG based on experimental data. Pinch analysis was proposed as a thermodynamic tool to analyze energy systems. Technique of pinch analysis have been successfully utilized to address cogeneration plants [15e18]. Townsend and Linnhoff [15,16] developed a methodology to size GTCP by matching grand composite curve (GCC) of the process with flue gas profile. Sarabchi and Polley [17], based on pinch analysis, suggested that regeneration should be employed only when heat is excess in flue gas exhaust from gas turbine. However, no methodology was suggested to compute regeneration potential. Bandyopadhyay et al. [18] proposed a pinch based approach to determine cogeneration potential for steam turbine cogeneration plant (STCP). Recently, techniques of pinch analysis are combined with the Rcurve representation [19e23], originally proposed by Kenny [5]. Kimura and Zhu [19] extended the R-curve concept to analyze cogeneration plants for retrofitting and grassroots cases. Varbanov et al. [20] proposed R-curve analysis for STCP, and suggested most appropriate utility system based on energy utilization factor (EUF). Ghannadzadeh et al. [21] proposed cogeneration targeting for site utility system using iterative method. Karimkashi and Amidpour [22] proposed plots of R-curve, R versus total cost, and R versus emission factor for design of cogeneration plants. For STCP, R-curve concept based on exergo-economic and exergo-environmental parameters are proposed by Navid et al. [23]. It may be noted that most of these works are directed towards analyzing STCP on Rcurve. Growing importance of GTCP necessitates appropriate thermodynamic optimization of such systems. It is important to develop an appropriate methodology to integrate gas turbine system with process plant. Primary objective of this paper is to propose such a methodology for appropriate integration of gas turbine, regenerator, and process streams and thereby reduce the overall fuel consumption. It may also be noted that due to significant difference in qualities of thermal energy and shaft work, a single metric is not always sufficient to analyze a CHP system. In this paper, a methodology based on pinch analysis is proposed to integrate gas turbine and regenerator with a process plant to minimize fuel consumption. Thermodynamic analysis of gas turbine integrated CHP plant is presented on novel diagram of gas turbine pressure ratio versus power to heat ratio diagram. Additionally, contour plots of energy utilization factors and fuel energy saving ratios are represented on this diagram for optimal
FESR ¼ 1
119
integration of gas turbine with a process plant. Optimum sizing of gas turbine integrated cogeneration plant for grassroots design and retrofitting are performed based on these diagrams. 2. Gas turbine based cogeneration plant (GTCP) Fig. 1 presents the schematic of GTCP with various components. Inlet air of mass flow rate ma (at ambient temperature, Ta and pressure, Pa) is compressed until pressure Paco (with a corresponding temperature of Taco) is reached. Then, air is heated in regenerator up to temperature Tareo using flue gas. Subsequently, preheated compressed air (Tareo) is used to burn fuel of mass flow rate mf in combustion chamber. The product of combustion termed as flue gas (mass flow rate mg) at a specified maximum temperature (Tgtm) is expanded in gas turbine to generate net work of WCG. The flue gas at gas turbine exit temperature (Tgto) supplies heat to the process streams and the regenerator. Thermal energy available in flue gas at gas turbine exhaust is always greater than or equal to required process heat duty (QP). This is achieved by maintaining mass flow rate of flue gas greater than or equal to the minimum mass flow rate required to satisfy process heat duty. The surplus energy available in flue gas at gas turbine exhaust is recirculated back into combustion chamber through regenerator (Qreg) as shown in Fig. 1. 2.1. Thermodynamic performance parameters As cogeneration involves two different forms of useful energies (viz. heat and power), it is difficult to define a single metric, as the qualities (according to the second law of thermodynamics) of these useful energies are different. To analyze the performance of cogeneration plants, following thermodynamic metrics are used: power to heat ratio (R), energy utilization factor (EUF), and fuel energy saving ratio (FESR) [6]. It may be noted that various other metrics are also proposed in literature. However, EUF and FESR are the two most important and widely used metrics. Power to heat ratio (R) is the ratio of net mechanical power output to the rate of process heat requirement.
R¼
net mechanical power output rate of process heat requirement
(1)
Energy utilization factor (EUF) [6] is the ratio of total useful energy (addition of the net mechanical power output and supplied process heat) to the total fuel energy supplied. Though, EUF recognizes importance of heat (thermal energy), it gives equal importance to heat and mechanical power, and not differentiate based on the second law of thermodynamics. It is used to plot Rcurves, initially proposed by Kenney [5], for thermodynamic analysis of various cogeneration plants.
EUF ¼
net mechanical power output þ process heat total fuel energy supplied
(2)
Fuel energy saving ratio (FESR) [6] is ratio of savings in fuel energy required to meet given mechanical power and heat by a CHP compared to conventional power plant and boiler separately supplying same amount of mechanical power and heat, to fuel energy required by conventional power plant and boiler for same output as that of CHP.
fuel energy required for cogeneration plant to generate power Wnet and heat QP fuel energy required for conventional plants to generate same power Wnet and heat QP
(3)
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Fig. 1. Schematic of gas turbine integrated cogeneration system.
Nesheim and Ertesva [24] called it relative primary energy savings. According to this criterion, two different cogeneration plants in terms of fuel energy savings can be compared. It also indicates societal benefits. 3. Problem definition The streams data of a process plant such as inlet, outlet temperatures, and heat capacity rates are given. The design data of gas turbine such as ambient temperature, maximum gas turbine temperature, specific heats and specific heat ratio of air and flue gas respectively, and lower calorific value of fuel are also known. GTCP generates work and supplies heat available in flue gas at the gas turbine exhaust to satisfy the complete hot utility requirement of the process plant. It is assumed that the heat available in the exhaust flue gas is always greater than or equal to the process heat requirement. This is accomplished by maintaining flue gas flow equals to or higher than the minimum required to satisfy the process heat. Regenerator is provided to improve the overall efficiency of the cogeneration system by preheating compressed air with the exhaust flue gas. The thermodynamic properties of air and flue gas such as specific heat capacities and ratios of specific heat capacities are determined at average temperature and are assumed constant. The objective is to develop a methodology to integrate the gas turbine, regenerator, and the process plant to minimize the overall fuel consumption. 4. Targeting of GTCP for minimum fuel consumption
ratio (Rmin). This minimal integration is analyzed in this subsection. For a fixed pressure ratio of gas turbine, flue gas temperatures at exit of compressor and turbine are determined using ideal gas law for known respective inlet temperatures and efficiencies. The process plant GCC is established using classical problem table algorithm (PTA) [26] or using modified problem table algorithm (MPTA) [27] at given minimum approach temperature and process streams data. The minimum flue gas flow rate can be targeted graphically by matching flue gas line drawn from flue gas temperature at gas turbine exit with process GCC [25,28], as shown in Fig. 2. The minimum mass flow rate of flue gas (mgmin) is given by following equation:
mgmin ¼
Q Qk p Cpg Tgto Tk DT 2
where, Qk and Tk are coordinates of one of the vertexes from process plant GCC and Cpg is specific heat capacity at constant pressure of flue gas. The point at which flue gas line touches process GCC is known as utility pinch (point 3 in Fig. 2) and temperature at that point termed as utility pinch temperature (Tp). However, the utility pinch point is not known a priori. Since utility pinch point is going to form at one of the vertexes of process plant GCC, flue gas (mgmin) can be calculated following Equation (4), for each vertex (k ¼ 1, …,l). The maximum of mass flow rate of flue gas calculated for each vertex represents the minimum mass flow rate of flue gas (mgmin). Mass balance of flue gas flow rate can be written as:
ma þ mf ¼ mg
An analytical methodology for energy integration of gas turbine and regenerator into process plant is developed in this section for the minimum fuel consumption. Methodology proposed by Varghese and Bandyopadhyay [25] for energy integration of fired heater with overall process is appropriately modified to apply for integration of gas turbine and regenerator into process plant. 4.1. Targeting GTCP at minimum power to heat ratio (Rmin) The heat available in flue gas at the outlet of gas turbine is transferred directly to cold streams of the process plant in process exchangers and to the compressed air in regenerator. If the heat availability from the flue gas at the exit of gas turbine is not sufficient to satisfy total process heat requirement then integration is termed as insufficient integration. The additional heat, in case of insufficient integration, can be provided either through auxiliary heating or by increasing flue gas flow rate. In this paper, insufficient integration is not considered. The minimum flow rate of flue gas, at which process heat is satisfied completely, is considered as the minimal integration and is represented by minimum power to heat
(4)
Fig. 2. Targeting of flue gas flow rate by matching with process plant GCC.
(5)
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121
The regenerated compressed air (at temperature, Tareo and mass flow rate, ma) is used for burning fuel in the combustion chamber. The flue gas temperature at exit of combustion chamber is Tgtm. The energy balance for combustion chamber [29] is given as:
ðTareo Ta Þma Cpa þ CV*hcc mf ¼
Tgtm Ta mg Cpg
(6)
where, CV is net calorific value of fuel, Cpa is specific heat capacity at constant pressure of air, and hcc is combustion efficiency. Ta is ambient temperature and not air temperature. Pinch analysis may be applied to determine compressed air temperature at regenerator outlet (Tareo), using the concept of the utility GCC [28]. Utility GCC is formed using utility streams such as flue gas and compressed air of integrated gas turbine. Fig. 3 illustrates the hot utility (temperature of flue gas from gas turbine exit, Tgto to stack, Tls) and cold utility (temperature of compressed air from compressor delivery, Taco to regenerator outlet, Tareo) composite curves. Similar to process plant GCC, the utility GCC is a plot of the enthalpy difference between the utility composites as shown in Fig. 3. It should be noted that the utility GCC is shown as reflected utility GCC (mirror image of utility GCC about vertical axis, see Fig. 3). This helps in matching it with process GCC to balance utility requirement as shown in Fig. 4. The matched process plant GCC and reflected utility GCC with other details such as hot and cold utility requirement, utility pinch points, and stack loss are shown in Fig. 4. All GCCs are plotted on shifted temperature scale with minimum approach temperature, DT. Air is heated from compressor delivery temperature (Taco) to regenerator temperature (Tareo) by flue gas. From energy balance at utility pinch point, regenerator outlet temperature, Tareo is determined as:
mg Cpg Tareo ¼
Tgto Ti DT 2 ma Cpa
Q P Qi
þ Tia
DT 2
(7)
where, Tia is compressed air temperature. If Ti < (Taco þ DT/2), then Tia ¼ (Taco þ DT/2), else Tia ¼ Ti. In general, Tia ¼ Maximum [(Taco þ DT/2), Ti]. The regenerator outlet temperature of air (Tareo) can be increased utmost up to flue gas temperature at gas turbine exit with approach temperature (Tgto DT). If compressor delivery temperature is higher than flue gas temperature at gas turbine exit, there is no regeneration and the regenerator outlet temperature of air (Tareo) is equal to compressor delivery temperature and is not determined by Equation (7). Once Tareo is determined, fuel consumption (mf) can be calculated using mass and energy balance of combustion chamber (Equation (6)). The mass flow rate of fuel consumption is determined at the minimum flue gas flow rate is represented as mfmin. Substituting Equations (4), (5) and (7) into Equation (6) and simplifying, mass flow rate of fuel consumption is given as:
QP
mfmin ¼
Qk Q P Tgto eTk
DT 2
Tgtm Tgto Ta þ Ti þ DT 2 CVhcc Cpa Tia
Cpa Cpg
DT 2
Fig. 3. Generation of utility GCC from utilities composite curves.
Fig. 4. Targeting of fuel consumption by matching of utility GCC with process plant GCC.
GCC. However, the utility pinch point is not known a priori. Since pinch is going to form at one of the vertexes of process plant GCC, fuel consumption (mfmin) can be calculated following Equation (8), for each vertex (i ¼ 1, …, l). The maximum of mass flow rate of fuel calculated for each vertex represents the minimum mass flow rate of fuel consumption (mfmin) for optimal integration of GTCP. The utility GCC touched at any of the vertex without intersection with process plant GCC forms optimal integration of gas turbine, regenerator, and process plant. This condition is satisfied for one of
Tia Ta
DT 2
þ Q p Qi (8)
Ta
where, Qi and Ti are the coordinates of one of the vertexes of process GCC and Tia is temperature of compressed air. QP is total process heat required and equals to the total hot utility of process plant
the vertexes, at which mass flow rate of fuel is the maximum, represents utility pinch. The other parameters R, EUF, and FESR are determined as follow:
122
R¼
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mg Cpg Tgtm Tgto ma Cpa ðTaco Ta Þ Qp
EUF ¼
mg Cpg Tgtm Tgto ma Cpa ðTaco Ta Þ þ Qp mf CV
(9)
by modifying equations provided in Section 4.1. At Rc, the compressed air temperature at regenerator outlet is equal to (Tgto DT), is substituted in Equation (7), and mass flow rate of air is determined by energy balance as:
(10) mg Cpg ma ¼
FESR ¼ 1
mf CV mg Cpg ðTgtm Tgto Þ ma Cpa ðTaco Ta Þ hPP
Q
(11)
þ hp B
Tgto Ti DT Q Q P i 2 Cpa Tgto Tia DT
Substituting Equations (5), (9) and (12) in Equation (6), and Tareo is replaced with (Tgto DT), Rc is calculated to be:
8 9 3 2 > > > > DT > > ð Taco eTa Þ Tgto eTi 2 > > 7 6 > > CV*h > > cc 7 6 > > T e T DT eT T gto a 4 gtm gto DT > Cpa > 5 T T > > gto ia 2 > > > > < = QP Qi þ ðTaco Ta Þ Rc ¼ 3 2 > QP Tgto eTia DT > > > CV*hcc DT > > e Tgto þDT þTa > > Cpa > > 7 6 Tgto eTi 2 > > CV*h > > cc 7 6 > > T e T e þ gtm a > > 5 4 Cpg Tgto e Tia e DT > > 2 > > : ;
For a given pressure ratio, Equation (9) determines R at the minimum flue gas flow rate, denoted as Rmin. Similarly, for all pressure ratios, minimum fuel consumption (mfmin), Rmin, EUF, and FESR are determined. Procedure of integration of GTCP is summarized as follows (flow chart of the same is shown in Fig. 5): Step 1 The process plant data and minimum approach temperature are given. With the help of MPTA [27] determine utilities requirements and plot process plant GCC. Step 2 For a specified pressure ratio of gas turbine, calculate outlet temperatures of compressor and gas turbine for known respective inlet temperatures and efficiencies. Step 3 Determine minimum mass flow rate of flue gas (mgmin) by Equation (4). Step 4 Determine mfmin from Equation (8). Also, compute other parameters such as Rmin, EUF, and FESR from Equations (9)e(11) respectively. Step 5 Similarly, determine mfmin, Rmin, EUF, and FESR for various pressure ratios and analyze thermodynamic performance of GTCP.
4.2. Targeting GTCP at critical regeneration limit (Rc) Heat availability increases with increasing mass flow rate in flue gas at any pressure ratio. This increased heat in flue gas, above the minimum required value, can be utilized through regeneration. By increasing flow rate of flue gas, compressed air can be heated maximum up to flue gas temperature at gas turbine exit with minimum approach temperature i.e. (Tgto DT). Increasing flue gas flow rate beyond a critical limit (mg at Rc) increases the stack losses and thereby, deteriorates overall energy efficiency of the system. The flue gas mass flow rate, at which compressed air is heated in regenerator up to (Tgto DT), is represented as critical flue gas flow rate, and corresponding critical R is denoted by Rc. The regeneration at Rc is termed as critical regeneration, where regeneration temperature is maximum possible with critical flue gas flow rate. It may be noted that the flue gas flow rate may be higher than the critical value if demand of shaft work is higher (i.e., R is higher than Rc). The critical mass flow rate of fuel consumption and Rc are determined
(12)
(13)
where, Qi and Ti are the coordinates of one of the vertexes from process GCC. Tia is same as mentioned in Section 4.1. Similar to Equation (8), utility pinch point is not known a priori, so Rc is determined following similar procedure. The regeneration is possible up to a pressure ratio, at which compressor delivery temperature (Taco) is equal to gas turbine exit temperature (Tgto) with approach temperature. This pressure ratio is referred as regeneration limiting pressure ratio (PRlimr). Beyond regeneration limiting pressure ratio, Rc equals to Rmin. Now, mf is established from Equations (5), (9), (12) and (13). The EUF and FESR are calculated from Equations (10) and (11) respectively.
4.3. Illustrative example 1 Consider GTCP with design data given in Table 1. Note that the net work generated by gas turbine is specified and is varied to illustrate the proposed methodology. The minimum approach temperature for process plant and utility GCC is 50 K. The hot utility requirement is 5000 kW with shifted pinch temperature of 398 K for the minimum approach temperature of 50 K. The problem is a threshold problem with no cold utility requirement. Data provided in Table 1 for gas turbine design is utilized to determine temperatures of air at compressor delivery and of flue gas at gas turbine exit. Theoretically possible minimum and maximum pressure ratios for GTCP are 1 and 105.8, respectively. Theoretical maximum pressure of gas turbine is constrained by the maximum temperature of process heating or compressor delivery temperature. In current problem, the maximum pressure ratio is constrained by the compressor delivery temperature, as above this pressure ratio compressor out let temperature is higher than turbine inlet temperature. The operating pressure of gas turbine plant is well below the theoretical maximum pressure ratio. At Rmin, if temperature of compressed air is less than actual process pinch temperature then compressed air is regenerated maximum up to actual process pinch temperature. At the minimum flue gas flow rate, regeneration is not achievable for pressure ratio higher than 1.95 due to Taco (Ti DT/2). The minimum mass flow rate of flue gas is targeted by using Equation (4). Following flow chart given in Fig. 5 and procedure outlined in Section 4.2, Rmin and Rc are determined appropriately for various pressure ratios.
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Fig. 5. Flow chart for targeting of GTCP at minimum flue gas flow rate.
The plot of pressure ratio (PR) versus R represents curves for Rmin and Rc with various integration regions of GTCP as shown in Fig. 6. As pressure ratio increases, Rmin also increases, and reaches a maximum. It reaches the maximum at a pressure ratio, where net work is highest. Subsequently with increasing pressure ratio further, Rmin decreases continuously still the theoretical maximum pressure ratio (provided theoretical maximum pressure ratio is higher than pressure ratio, at which specific net work is maximum). As pressure ratio increases, Rc also increases, reaches a maximum and then decreases till it coincides with Rmin curve. Rc and Rmin curves coincide with each other when the limiting regeneration pressure ratio is reached. For this example, limiting regeneration pressure ratio (PRlimr) is 15.3. Above limiting regeneration pressure ratio (PRlimr ¼ 15.3), there is no regeneration region. The region towards left of Rmin curve represents insufficient integration where process heat demand is not satisfied. The region outside of Rc
(towards right), due to high flue gas flow rate and constraint of maximum regeneration temperature, represents high stack loss. The intersection region of Rmin and Rc is feasible region for integration of gas turbine, regenerator, and process plant as shown in Fig. 6. 4.4. Thermodynamic analysis of GTCP To analyze thermodynamic performance of GTCP, variations of EUF and FESR with pressure ratios are studied. To determine contours of EUF and FESR at various pressure ratios by changing flue gas flow rate (mg mgmin), equations developed in previous sub-
Table 1 Gas turbine design data. Maximum gas turbine inlet temperature (Tgtm), K Atmospheric air temperature (Ta), K Gas turbine efficiency (hT) Minimum approach temperature for all GCCs (DT), K Specific heat capacity at constant pressure gas (Cpg), kW/kgK Ratio of specific heat capacities gas (gg) Thermal efficiency of standard plant (hPP) Stream generator efficiency (hB)
1373
298 0.9 50
Specific heat capacity at constant pressure air (Cpa), kW/kgK Process heat duty (Qp), kW Compressor efficiency (hc) Ratio of specific heat capacities air (ga)
1.148 Combustion efficiency of GT (hcc) 1.33 0.36 0.9
Stack temperature (Ts), K Lower calorific value of fuel (CV), kJ/kg
1.005
5000 0.85 1.4
0.98
393 41,000 Fig. 6. Various integration regions for GTCP of example 1.
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sections are modified. From Equations (5) and (7), regeneration temperature is determined to be:
! Tareo ¼
mg Cpg
CVhcc CVhcc DT T DT cc Ta þ CVh T T T T Q þ T þ Q gto gtm a a P i i ia Cpa Cpg Cpa 2 2 CVhcc QP Qi mg Cpg Tgto Ti DT 2 Tgtm þ Ta þ Cpg
where, Qi and Ti are the coordinates of one of the vertexes of process GCC. Calculation of Tia is described in sub-Section 4.1. The regenerator outlet temperature of air (Tareo) can be increased utmost up to flue gas temperature at gas turbine exit with approach temperature (Tgto DT). If compressor delivery temperature is higher than flue gas temperature at gas turbine exit, there is no regeneration and the regenerator outlet temperature of air (Tareo) is equal to compressor delivery temperature. In general, Tareo is determined by following condition:
Tareo ¼
8 > < Taco
procedure to determine data for a range of constant EUF at various pressure ratios.
! > ; : MIN Tareo
Tgto
DT 2
If Tgto Taco otherwise
(15)
Mass flow rates of fuel consumption, and compressed air may be calculated using Equations (5), (6) and (15). Subsequently, R, EUF, and FESR can be determined for any given pressure ratio and flue gas flow rate. Flow chart shown in Fig. 7 represents systematic
(14)
4.4.1. Revisiting example 1 Study the behavior of EUF using PR versus R curve. All data of GTCP and process plant are same as given in example 1. Using procedure given in flow chart (Fig. 7), the data for constant EUF is obtained. The contours of EUF are created by plotting data of various constant EUF on PR versus R plot as shown in Fig. 8. The nature of constant EUF curves for higher values is similar to Rmin curve. The flue gas flow rate is less at lower R, and hence stack loss are lower, results in higher EUF (see Fig. 8 for EUF ¼ 0.8). On the other hand, lower values of constant EUF lines show similar nature as that of Rc curve with higher R (see Fig. 8 for constant EUF at 0.6). Lower EUF indicates higher stack loss due to higher flue gas flow rate. In addition to this, maximum regeneration temperature limit is reached at Rc, so for higher R (>Rc), stack loss are further increased. The highest value of EUF is at pressure ratio 1 and R equal to zero, represented by rhombus in Fig. 8. For pressure ratio 1, GTCP works as fired heater. Procedure of data generation for constant FESR curve is also given in flowchart of Fig. 7. In this, mass flow rate is varied until
Fig. 7. Flow chart to generate contours of EUF/FESR on PR versus R plot.
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which remains constant with further increasing R. It is interesting to note that though the contour plots of energy utilization factors and fuel energy saving ratios differ significantly, loci of the maximal energy utilization factor and the maximal fuel energy saving ratio are identical as shown in Fig. 10. The EUF and FESR are given in terms of R as follows:
EUF ¼
Q P ð1 þ RÞ mf CV
FESR ¼ 1 QP
(16)
mf CV
R hPP
þ
(17)
1 hB
From Equations (16) and (17), relationship between EUF and FESR is written as: Fig. 8. Contour of EUF for integrated GTCP of example 1.
FESR ¼ 1 EUF
FESR determined by Equation (11) is matched with fixed FESR. For some of the pressure ratios, there are two values of FESR, as FESR increases from minimum value (corresponding to mgmin) to maximum and then decreases with increase in flue gas flow rate, unlike EUF for a given pressure ratio. The searching two values of FESR for typical pressure ratios are important. The contours of FESR are generated by data of various constant FESR on PR versus R plot as shown in Fig. 9. The contours of FESR start from Rmin curve. With increase in R, pressure ratio for constant FESR curve decreases still it intersects Rc at minimal pressure ratio. Further increasing R, pressure ratio increases continuously, however, R reaches maximum and starts decreasing following nature of Rc curve (see FESR ¼ 0.2 and 0.25 in Fig. 9). A constant FESR curve for large values starts from Rc, and also ends at Rc as shown in Fig. 9 for FESR ¼ 0.35. The highest value of FESR is a point (0.353) represented by rhombus as shown in Fig. 9. The maximum EUF and FESR are determined for various pressure ratios considering flue gas flow rate as variable at a given pressure ratio. This curve starts at pressure ratio equals to 1 and R equals to zero. With increasing pressure ratio, R increases, following Rmin curve up to a pressure ratio, at which specific net work is maximum. Then this curve is shifted to Rc curve, as pressure ratio decreases with increasing R. It leaves Rc curve at pressure ratio 4.53,
Fig. 9. Contour of FESR for integrated GTCP of example 1.
1þR
R hPP
þ
(18)
1 hB
Equation (18) shows that for given R, EUF and FESR are proportional to each other assuming standard power plant and boiler plant efficiencies constant. Due to this, in pressure ratio versus R plot, both curves of maximum EUF and FESR are identical as shown in Fig. 10. In retrofitting case, where process heating is to be implemented, pressure ratio of gas turbine plant is known. The horizontal line dropped from a given pressure ratio, intersects maximum EUF and FESR curve at two places with two values of R to design cogeneration system. As shown in Fig. 10, horizontal line dropped from pressure ratio PR1 intersects maximum EUF and FESR curve at R1 and R2, where R1 < R2. At same pressure ratio, specific work is constant, so lower value of R (R1) represents lower flue gas flow rate and hence lesser stack loss. Designing system at R1 gives higher EUF, which indicates lower fuel consumption with lower operating cost. On the other hand, designing system at R2, represents higher FESR as R2 is at critical regeneration limit. This signifies higher work out and higher societal benefits. There is Pareto optimality between higher EUF and higher FESR based on design objective and hence decision maker's role is important.
Fig. 10. Designing of integrated gas turbine, regenerator, and process plant for example 1.
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Table 2 Process plant data (minimum approach temperature ¼ 50 K). Streams
Ts, K
Tt, K
C, kW/K
Heat duty, kW
H1 H2 H3 C1 C2
675 575 575 315 315
375 375 365 675 575
100 82.5 10 60 120
30,000 16,500 2100 21,600 31,200
For a new design, power to heat ratio (R) can be determined easily. For this value of power to heat ratio (R), there is unique value of the maximum EUF and FESR with corresponding pressure ratio for optimal design of GTCP. If vertical line dropped from a given value of R falls on maximum EUF and FESR curve which is part of Rc curve with higher FESR, else R drops on maximum EUF and FESR curve which is part of Rmin curve with higher EUF and lower fuel consumption. For any R, outside the range of critical regeneration limit (Rc) at maximum EUF and FESR curve (see Fig. 10, Rpl), there is very high stack loss. Similarly, for pressure ratio outside the range of maximum EUF and FESR curve (PR > PRl, see Fig. 10), stack loss is higher. For PR > PRlimr (see Fig. 10), there is no regeneration, and hence very high stack losses.
Fig. 12. Contour of FESR for integrated GTCP of example 2.
Table 2 gives process streams data such as inlet-outlet temperatures, heat capacity rate, and heat duty of the process plant. The minimum approach temperature for all integrations is 50 K. Using MPTA [27], hot and cold utilities requirement are determined to be 5000 and 800 kW respectively with shifted pinch temperature 550 K. The total heat demand of process plant 5000 kW is satisfied by flue gas exhaust from gas turbine by direct heat transfer using counter current heat exchanger. Gas turbine design data given in Table 1 is applied to determine temperatures of compressed air at compressor delivery and flue gas at gas turbine outlet. The procedure given in Section 4 is used to determine various parameters and from them various graphs are plotted. The variation of Rmin and Rc on PR versus R plot represents the different regions of integration as shown in Fig. 11. The overall nature of curves is similar to previously shown for example 1. Compared to example 1, in this example, process pinch temperature and process heat requirements are at elevated temperature. Additionally, it is observed that utility pinch point is changed from one vertex to another
vertex for typical values of pressure ratios and power to heat ratio. The change in pinch point from one vertex to another vertex is termed as shift of pinch point or pinch jump. Due to process heat requirement at elevated temperature, the maximum pressure ratio for integration with process plant is limited up to 19.5. In addition to this, for requirement of process heat at higher temperature, flue gas flow rate required is also high, increasing values of R. The first peak in Rc curve is due to shift of utility pinch point at pressure ratio 6.16 and R to be 4.3. Due to shift of utility pinch point, the pinch point temperature increases, increasing flue gas flow rate, R, and pressure ratio. This results in diverging of remaining part of Rmin and Rc curves outwards as shown in Fig. 11 (see points P1 and P2). The contour for EUF can be generated similar to Fig. 8 (for brevity it is not shown). The contour for FESR is shown in Fig. 12. Due to shift of pinch points, the shape of contour plots are changed, however overall nature is remained same. Additionally, it is observed that maximum EUF and FESR curve plotted on pressure ratio versus R, overlap exactly as shown in Fig. 13. It starts from Rmin curve with pressure ratio equals to 1 and R equals to zero. The maximum EUF and FESR curve moves along Rmin curve, and both R and pressure ratio increases. Then it translates to Rc curve, following Rc curve with increasing pressure ratio and R. At the end, it leaves Rc curve at pressure ratio 4.53 with further increase of R, same as observed earlier for example 1. At higher R, (>Rpl),
Fig. 11. Various integration regions for GTCP of example 2.
Fig. 13. Designing of integrated gas turbine, regenerator, and process plant for example 2.
5. Illustrative example 2
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compared to process heat, power generation is very high, reducing Equation (16) of EUF to the equation of power plant efficiency. This represents integrated gas turbine system behaves as gas turbine power plant with regeneration following characteristics of gas turbine power plant. It is important to note that at lower pressure ratio, the efficiency of gas turbine power plant with regeneration is highest (for example 1 and 2, pressure ratio is 4.53 at 1373 K maximum temperature), similar observation is reported by Saravanamuttoo et al. [29]. In general, GTCP should be designed between optimal pressure ratio (PRopt) at which power plant efficiency is maximum and limiting pressure ratio (PRl) at which specific net work is maximum. There may be tradeoff between gas turbine power plant efficiency, and its size and weight. Gas turbine power plant designed at optimal pressure for maximum efficiency requires higher size and capacity due to lower specific net work. On the other hand, system designed at pressure ratio for maximum specific net work, pressure ratio is higher with heavy compressor and lower efficiency. 6. Conclusion A methodology is proposed to integrate gas turbine and regenerator with process plant directly at minimum fuel consumption. In addition to this, thermodynamic analysis of GTCP with regeneration is presented on gas turbine pressure ratio versus power to heat ratio diagram. On this novel diagram, limits of integration are identified and various regions of integration are presented such as infeasible integration, feasible integration, high stack, and no regenerator. Additionally, contour plots of energy utilization factors and fuel energy saving ratios are represented on this diagram for optimal integration of gas turbine with a process plant. It is interesting to note that though the contour plots of energy utilization factors and fuel energy saving ratios differ significantly, loci of the maximal energy utilization factor and the maximal fuel energy saving ratio are identical. It is noted that GTCP with regeneration is thermodynamically efficient at lower pressure ratios. The proposed analysis (maximum EUF and FESR plot on pressure ratio vs. R) can be used for retrofitting and grassroots design to select optimal configuration of GTCP. In grassroots design of GTCP, for a given R, optimal pressure ratio can be selected based on maximum EUF and FESR. The retrofitting case, for known pressure ratio, there are two values of R. Optimal R can be decided based on the objective of designer such as operating cost to be minimum or fuel energy savings (societal benefits) to be maximum. The shift of pinch point influences the sizing of GTCP as shown by example 2. At very high R, GTCP plant behaves similar to gas turbine plant with regeneration. The maximum EUF and FESR are at maximum power plant efficiency with constant optimal pressure ratio for very high values of R (>Rl). The optimal pressure ratio for maximum power plant efficiency is lower than limiting pressure ratio at which specific net work is maximum. There may be tradeoff between gas turbine power plant efficiency, and its size and weight. Gas turbine power plant designed at optimal pressure for maximum power plant efficiency requires higher size and capacity due to lower specific net work. On the other hand, system designed for maximum specific net work requires high pressure ratio with heavy compressor and low power plant efficiency. Nomenclatures Cp CV m q/Q R
specific heat at constant pressure (kJ/kgK) net calorific value (kJ/kg) mass flow rate (kg/s) heat duty (kW) ratio of power to heat rate
T W
127
temperature (K) mechanical power (kW)
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